I dug out the RAeS Journal of Aeronautical History 2013 Paper 'The HAWK story' to see if it has anything to say about the origin of the name, it doesn't. In case anyone is interested in reading it, I checked that it is still available online; it is at:
https://www.aerosociety.com/media/48...hawk-story.pdf
It concludes with a copy of a letter from the late Duncan Simpson in which he relates the first flight (XX154) and the first delivery to Valley with CinC Training Command onboard.
Hawk XX163 was delivered to RAF Valley on 4th November 1976. The Commander-in-Chief [ACM Sir Rex Roe GCB, AFC] had requested to participate in this flight – which he duly did.
We arrived at Valley, in heavy rain, to be welcomed by Group Captain Thornton and his instructors.
So began the illustrious career in the Royal Air Force and overseas services, not forgetting the Red Arrows, of this splendid aeroplane.
In T2 form we shall see more of it in the future.